Two sets F and G satisfy the following conditions:
F = {(x, y): y = 5x + 7},
G = {(x, y): y = mx + c}
F intersection G = {}
Write down the value of m and a possible value for c
Since F and G do not have any common points (F intersection G = {}), it means that the line represented by G does not intersect with the line represented by F.
The line represented by F has a slope of 5, which means m = 5.
A possible value for c can be any number different from 7, since 7 is the y-intercept of the line represented by F (y = 5x + 7). For example, we can choose c = 0.
So, the value of m is 5 and a possible value for c is 0.
To find the value of m and a possible value for c, we need to determine the equation of set G and find its intersection with set F.
Since F is given as y = 5x + 7, we can see that m = 5 and c = 7.
Now, let's determine the equation of set G:
G = {(x, y): y = mx + c}
Since we want the intersection of F and G to be an empty set (F ∩ G = {}), this means the two lines represented by F and G do not have any common points or do not intersect.
So, any value for m and c would satisfy the condition F ∩ G = {}. One possible value for c could be any number that is not equal to 7, such as c = 0.
Therefore, the value of m is 5, and a possible value for c is 0.